The following rules should be observed throughout the assignment: • Each polynom
ID: 3853781 • Letter: T
Question
The following rules should be observed throughout the assignment:
• Each polynomial should be represented as a singly-linked list (see files “list.h” and “list.c” from the book).
• Each element in the linked list should represent one of the terms in the polynomial.
• The data held by each element should be type double representing the constant for that term.
• For example, the polynomial 6.0x3 - 5.3x + 3.1 would be represented by the linked list 6.0 0.0 -5.3 3.1.
a) (1 point) Implement a function called appendTerm:
void appendTerm(List *pPolynomial, double constant);
This function should append (insert at the end) the value constant to pPolynomial. For example, appending 3.1 to pPolynomial already containing 6.0 0.0 -5.3 should result in the value 3.1 being added at the end: 6.0 0.0 -5.3 3.1. If the append fails the program should exit.
b) (2 points) Implement a function called display:
void display(List *pPolynomial);
This function should output the polynomial to stdout in proper polynomial format. For example, displaying polynomial 6.0 0.0 -5.3 3.1 should result in 6.0x^3 - 5.3x + 3.1 being output.
c) (2 points) Implement a function called evaluate:
double evaluate(List *pPolynomial, double x);
This function should evaluate the polynomial for the given value of x and return the result. For example, given polynomial 6.0 0.0 -5.3 3.1 and x having value 7.0 the function should return 2024.0 (the result of evaluating 6.0*7.03 - 5.3*7.0 + 3.1).
d) (4 points) Write a program to test the functions from parts a – c. Your test program should demonstrate creating, displaying, and evaluating the following polynomials with the given values for x:
• x + 1.0 with x = 1.0
• x 2 - 1.0 with x = 2.03
• -3.0x3 + 0.5x2 - 2.0x with x = 05.0
• -0.3125x4 - 9.915x2 - 7.75x - 40.0 with x = 123.45
e. (1 point) Make sure your source code is well-commented, consistently formatted, uses no magic numbers/values, follows programming best-practices, and is ANSI-compliant.
Explanation / Answer
#include<iostream>
#include<stdlib.h>
#include<math.h>
using namespace std;
void appendTerm(List *pPolynomial, double constant)//method to append value to list
{
List *t=pPolynomial;
if(pPolynomial==NULL)//initially list must be empty
{
pPolynomial = (List*)malloc(sizeof(List));//creating new node
if(pPolynomial==NULL)//if append fails then exit
exit(0);
pPolynomial.c = constant;//assigning value to new node
pPolynomial.next = NULL;
}
else//if list is not empty
{
while(t->next !=NULL)
{
t=t->next;
}//moving to last node
//creating new node
t->next = (List*)malloc(sizeof(List));//appending new node to list
if(t->next==NULL)//if append fails then exit
exit(0);
t->next.c = constant;//assigning value to new node
t->next->next = NULL;//setting next value to constant..
}
}
void display(List *pPolynomial)
{
List *t = pPolynomial;
while(t!=NULL)//loop to traverse list
{
cout<<t->c<<" ";//printing values of the list
t=t->next;//moving to next node
}
cout<<" ";
return ;
}
//method which recursively evaluates the polynomial..
double evaluate(List *pPolynomial, double x)//method to evaluate polynomial for given x value..
{
static int i=0;
double value;
if(pPolynomial==NULL)
return 0;
value = evaluate(pPolynomial->next,x);
value = value+pPolynomial->c * pow(x,i);
i++;
return value;
}
int main()
{
List *p;
appendTerm(p,6);
appendTerm(p,0);
appendTerm(p,-5.3);
appendTerm(p,3.1);
display(p);
cout<<evaluate(p,7)<<endl;//evaluating polynomial
//similary for other polynomials also
List *q;
appendTerm(q,1);
appendTerm(q,1);
display(q);
cout<<evaluate(q,1)<<endl;//evaluating polynomial
List *m;
appendTerm(m,1);
appendTerm(m,0);
appendTerm(m,1);
display(m);
cout<<evaluate(m,2.03)<<endl;//evaluating polynomial
List *n;
appendTerm(n,-3);
appendTerm(n,0.5);
appendTerm(n,-2);
appendTerm(n,0);
display(n);
cout<<evaluate(n,5)<<endl;//evaluating polynomial
List *o;
appendTerm(o,-0.3125);
appendTerm(o,0);
appendTerm(o, - 9.915);
appendTerm(o,- 7.75);
appendTerm(o,- 40.0 );
display(o);
cout<<evaluate(o,123.45 )<<endl;//evaluating polynomial
///then append the value..
return 0;
}
//note: to run this code you should first include list.h or list.c